Uniform approximation for diffractive contributions to the trace formula in billiard systems

Details Uniform approximation for diffractive contributions to the trace formula in billiard systems Uniform approximation for diffractive contributions to the trace formula in billiard systems

1996-10-02

arxiv.org/abs/chao-dyn/9610006v1

Nonlinear Sciences

Chaotic Dynamics

LaTeX, 41 pages including 12 PostScript figures, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.55.2279

We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional billiard systems with corners. This is achieved by using the exact Sommerfeld solution for the Green function of a wedge. We obtain a uniformly valid formula which interpolates between formerly separate approaches (the geometrical theory of diffraction and Gutzwiller's trace formula). It yields excellent numerical agreement with exact quantum results, also in cases where other methods fail.

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